JavaScript (ES6), 3739 3133 bytes
f=(n,j=0,k=1)=>n>j?f(n,k,j+k)+1:0
Even with ES7, the inverse Binet formula takes 47 bytes:
x=>Math.log(x*5**.5)/Math.log(.5+1.25**.5)+.5|0
x=>Math.log(x*5**.5)/Math.log((1+5**.5)/2)+.5|0
x=>Math.log(x*(p=5**.5))/Math.log((1+p)/2)+.5|0